Smooth Shape-Aware Functions with Controlled Extrema

dc.contributor.authorJacobson, Alecen_US
dc.contributor.authorWeinkauf, Tinoen_US
dc.contributor.authorSorkine, Olgaen_US
dc.contributor.editorEitan Grinspun and Niloy Mitraen_US
dc.date.accessioned2015-02-28T07:44:05Z
dc.date.available2015-02-28T07:44:05Z
dc.date.issued2012en_US
dc.description.abstractFunctions that optimize Laplacian-based energies have become popular in geometry processing, e.g. for shape deformation, smoothing, multiscale kernel construction and interpolation. Minimizers of Dirichlet energies, or solutions of Laplace equations, are harmonic functions that enjoy the maximum principle, ensuring no spurious local extrema in the interior of the solved domain occur. However, these functions are only C0 at the constrained points, which often causes smoothness problems. For this reason, many applications optimize higher-order Laplacian energies such as biharmonic or triharmonic. Their minimizers exhibit increasing orders of continuity but lose the maximum principle and show oscillations. In this work, we identify characteristic artifacts caused by spurious local extrema, and provide a framework for minimizing quadratic energies on manifolds while constraining the solution to obey the maximum principle in the solved region. Our framework allows the user to specify locations and values of desired local maxima and minima, while preventing any other local extrema. We demonstrate our method on the smoothness energies corresponding to popular polyharmonic functions and show its usefulness for fast handle-based shape deformation, controllable color diffusion, and topologically-constrained data smoothing.en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume31
dc.identifier.doi10.1111/j.1467-8659.2012.03163.x
dc.identifier.issn1467-8659en_US
dc.identifier.urihttps://doi.org/10.1111/j.1467-8659.2012.03163.xen_US
dc.publisherThe Eurographics Association and Blackwell Publishing Ltd.en_US
dc.subjectI.3.5 [Computer Graphics]en_US
dc.subjectComputational Geometry and Object Modelingen_US
dc.subjectGeometric algorithmsen_US
dc.subjectlanguagesen_US
dc.subjectand systemsen_US
dc.titleSmooth Shape-Aware Functions with Controlled Extremaen_US
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